Experimental Test of the Differential Fluctuation Theorem and a Generalized Jarzynski Equality for Arbitrary Initial States

Hoang, Thai M.; Pan, Rui; Ahn, Jonghoon; Bang, Jaehoon; Quan, H. T.; Li, Tongcang

doi:10.1103/physrevlett.120.080602

Cited by 104 publications

(71 citation statements)

References 39 publications

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“…Heat or work along the stochastic trajectory may need to be measured experimentally for small systems with odd controlling parameters to determine which scheme is more suitable. Differential fluctuation theorem has been experimentally verified in both underdamped and overdamped situations for systems con-taining only even controlling parameters [58]. Similar experiment may be conducted for small systems with odd controlling parameters to answer the question above.…”

Section: Conclusion and Discussionmentioning

confidence: 83%

Stochastic thermodynamics with odd controlling parameters

2019

Phys. Rev. E

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Stochastic thermodynamics extends the notions and relations of classical thermodynamics to small systems that experience strong fluctuations. The definitions of work and heat and the microscopically reversible condition are two key concepts in the current framework of stochastic thermodynamics. Herein, we apply stochastic thermodynamics to small systems with odd controlling parameters and find that the definition of heat and the microscopically reversible condition are incompatible. Such a contradiction also leads to a revision to the fluctuation theorems and nonequilibrium work relations. By introducing adjoint dynamics, we find that the total entropy production can be separated into three parts, with two of them satisfying the integral fluctuation theorem. Revising the definitions of work and heat and the microscopically reversible condition allows us to derive two sets of modified nonequilibrium work relations, including the Jarzynski equality, the detailed Crooks work relation, and the integral Crooks work relation. We consider the strategy of shortcuts to isothermality as an example and give a more sophisticated explanation for the Jarzynski-like equality derived from shortcuts to isothermality.

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Section: Conclusion and Discussionmentioning

confidence: 83%

Stochastic thermodynamics with odd controlling parameters

2019

Phys. Rev. E

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“…As an another demonstration on how the formalism can help us obtain statistical properties of EP-related quantities, we note that there is another generally valid FR called differential fluctuation theorem for the work done by the system W , derived in [32,33] and experimental verified in [57] for detailed balanced systems. Here we provide a more general derivation to extend it to nondetailed balanced systems.…”

Section: H Two Fluctuation Relations For Heat and Workmentioning

confidence: 97%

Unified formalism for entropy production and fluctuation relations

Yang

Qian

2020

Phys. Rev. E

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Stochastic entropy production, which quantifies the difference between the probabilities of trajectories of a stochastic dynamics and its time reversals, has a central role in nonequilibrium thermodynamics. In the theory of probability, the change in the statistical properties of observables due to reversals can be represented by a change in the probability measure. We consider operators on the space of probability measure that induce changes in the statistical properties of a process, and formulate entropy productions in terms of these change-of-probability-measure (CPM) operators. This mathematical underpinning of the origin of entropy productions allows us to achieve an organization of various forms of fluctuation relations: All entropy productions have a non-negative mean value, admit the integral fluctuation theorem, and satisfy a rather general fluctuation relation. Other results such as the transient fluctuation theorem and detailed fluctuation theorems then are derived from the general fluctuation relation with more constraints on the operator of a entropy production. We use a discrete-time, discrete-state-space Markov process to draw the contradistinction among three reversals of a process: time reversal, protocol reversal and the dual process. The properties of their corresponding CPM operators are examined, and the domains of validity of various fluctuation relations for entropy productions in physics and chemistry are revealed. We also show that our CPM operator formalism can help us rather easily extend other fluctuations relations for excess work and heat, discuss the martingale properties of entropy productions, and derive the stochastic integral formulas for entropy productions in constant-noise diffusion process with Girsanov theorem. Our formalism provides a general and concise way to study the properties of entropy-related quantities in stochastic thermodynamics and information theory. *

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“…In addition, DFA yields better estimates for the long-range auto-correlations than other techniques, such as the auto-correlation function, especially for short time series [7]. On the other hand, under certain conditions, the fluctuation-dissipation theorem for the dynamic systems in the stationary state provides a theoretical relation between the response to small external perturbations and the spontaneous fluctuations, but no general results are available for the dynamic systems in non-stationary states [8][9][10][11][12][13]. For dynamic systems, the general problem whether and how the past dynamic fluctuations affect the future motion of the dynamic variables is crucial, and remains challenging, especially in the cases that the equations of motion are unknown.…”

Section: Introductionmentioning

confidence: 99%

Temporal correlation functions of dynamic systems in non-stationary states

Chen

Zheng

et al. 2018

New J. Phys.

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Besides the fluctuation-dissipation theorem around the stationary state, how the fluctuations in nonstationary states correlate with the future motion of the dynamic variables remains a challenging problem. Further, most temporal correlations of the dynamic variables are zero or very weak in a large class of dynamic systems if the dynamic effects of non-stationary states are not considered. We propose novel methods to compute the temporal correlation functions taking into account the dynamic effects of the non-stationary states. In various dynamic systems, we reveal that the past dynamic fluctuations do drive the future motion of the dynamic variables. This dynamic effect of the non-stationary states is a robust, intrinsic and important property of the complex dynamic systems.

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Experimental Test of the Differential Fluctuation Theorem and a Generalized Jarzynski Equality for Arbitrary Initial States

Cited by 104 publications

References 39 publications

Stochastic thermodynamics with odd controlling parameters

Stochastic thermodynamics with odd controlling parameters

Unified formalism for entropy production and fluctuation relations

Temporal correlation functions of dynamic systems in non-stationary states

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